2 The Swiss The dataset \"chickwts\" you can access in R by typing head (sviss)

Question

2 The Swiss The dataset "chickwts" you can access in R by typing head (sviss) It has 6 variables, and 47 observations. Let X... X% be random variables for the 6 different columns. Let and be estimators for the mean and variance of each of the variables. Let be the Covariance between any two of the columns. Estimate all the - pairwise - some comments. Make Do any of the variables appear to be independent. Why or why not?

Explanation / Answer

> data(swiss) > head(swiss) Fertility Agriculture Examination Education Catholic Courtelary 80.2 17.0 15 12 9.96 Delemont 83.1 45.1 6 9 84.84 Franches-Mnt 92.5 39.7 5 5 93.40 Moutier 85.8 36.5 12 7 33.77 Neuveville 76.9 43.5 17 15 5.16 Porrentruy 76.1 35.3 9 7 90.57 Infant.Mortality Courtelary 22.2 Delemont 22.2 Franches-Mnt 20.2 Moutier 20.3 Neuveville 20.6 Porrentruy 26.6 > x1=swiss$Fertility > x2=swiss$Agriculture > x3=swiss$Examination > x4=swiss$Education > x5=swiss$Catholic > x6=swiss$Infant.Mortality > n=length(x1) > x=list(x1,x2,x3,x4,x5,x6) > print ("means") [1] "means" > sapply(x,mean) [1] 70.14255 50.65957 16.48936 10.97872 41.14383 19.94255 > print ("Variances") [1] "Variances" > (n*sapply(x,var)/(n-1)) [1] 159.434726 527.012448 65.030246 94.465974 1777.105288 [6] 8.668233 > cov(x1,x2) [1] 100.1691 > cov(x1,x3) [1] -64.36693 > cov(x1,x4) [1] -79.72951 > cov(x1,x5) [1] 241.5632 > cov(x1,x6) [1] 15.15619 > cov(x2,x3) [1] -124.3928 > cov(x2,x4) [1] -139.6574 > cov(x2,x5) [1] 379.9044 > cov(x2,x5) [1] 379.9044 > cov(x2,x6) [1] -4.025851 > cov(x3,x4) [1] 53.57586 > cov(x3,x5) [1] -190.5606 > cov(x3,x5) [1] -190.5606 > cov(x3,x6) [1] -2.649537 > cov(x4,x5) [1] -61.69883 > cov(x4,x5) [1] -61.69883 > cov(x4,x6) [1] -2.781684 > cov(x5,x6) [1] 21.31812

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